An triangular prism has base xcm, height (x+4)cm and length 4xcm. Find the volume of the prism in terms of x. Find the volume when x=2cm.

This question combines knowledge of volume equations with using unknown variables. We know the volume of a prism is the area of the face multiplied by the length. The first step would be to find the area of the triangular face, using the area of a triangle, 1/2 * base * height = area. 1/2 * b * h = 1/2 * (x) * (x+4) = 1/2* (x² + 4x) = 1/2x² + 2x cm²Next we find the volume of the prism by multiplying this expression by the length, 4x cm. length * area = 4x * (1/2x² + 2x) = 2x³ + 8x² cm³We now have an expression for the volume with an unknown x. Next, we can substitute x=2 into the expression. 2*(2)³+ 8*(2)²= 28 + 84 = 16 + 32 = 48cm³